If it became law, the proposal would lift the threat of federal prosecution from people who use medical marijuana in states where it is legal to do so, even though the bill does not legalize it in other states.

Currently, medical marijuana is legal in 23 states and the District of Columbia.

The legislation highlights a paradox between state and federal laws. Medical marijuana is still on the federal government’s list of banned substances, despite dozens of states around the country legalizing it.

In some cases, this has enabled federal prosecutors to charge medical marijuana patients who were following their states’ rules.

The Obama administration has said it will not enforce the federal laws against medical marijuana. However, any future president could change that policy.

Last year, Congress adopted a policy in the appropriations bill saying it would not fund federal enforcement against medical marijuana patients.

However, the new proposal is the first fully-fledged legislative attempt at the federal level to allow medical marijuana in some states, sources say.

"The introduction of this legislation in the Senate demonstrates just how seriously this issue is being taken on Capitol Hill,” said Dan Riffle, director of federal policies at the Marijuana Policy Project, a group that advocates for liberalizing marijuana laws.

The senators will annouce more details about the bill during a Tuesday press conference.